| Title:
|
Homomorphic images of finite subdirectly irreducible unary algebras (English) |
| Author:
|
Ježek, J. |
| Author:
|
Marković, P. |
| Author:
|
Stanovský, D. |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
57 |
| Issue:
|
2 |
| Year:
|
2007 |
| Pages:
|
671-677 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We prove that a finite unary algebra with at least two operation symbols is a homomorphic image of a (finite) subdirectly irreducible algebra if and only if the intersection of all its subalgebras which have at least two elements is nonempty. (English) |
| Keyword:
|
subdirectly irreducible unary algebra |
| MSC:
|
08A60 |
| MSC:
|
08B26 |
| idZBL:
|
Zbl 1174.08304 |
| idMR:
|
MR2337621 |
| . |
| Date available:
|
2009-09-24T11:48:21Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/128196 |
| . |
| Reference:
|
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| Reference:
|
[2] J. Ježek, T. Kepka: The factor of a subdirectly irreducible algebra through its monolith.Algebra Universalis 47 (2002), 319–327. MR 1918733, 10.1007/s00012-002-8192-1 |
| Reference:
|
[3] T. Kepka: On a class of subdirectly irreducible groupoids.Acta Univ. Carolinae Math. Phys. 22 (1981), 17–24. Zbl 0478.08005, MR 0635973 |
| Reference:
|
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| Reference:
|
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| Reference:
|
[6] R. McKenzie, G. McNulty, and W. Taylor: Algebras, Lattices, Varieties, Volume I.Wadsworth & Brooks/Cole, Monterey, 1987. MR 0883644 |
| Reference:
|
[7] R. McKenzie, D. Stanovský: Every quasigroup is isomorphic to a subdirectly irreducible quasigroup modulo its monolith.Acta Sci. Math. (Szeged) 72 (2006), 59–64. MR 2249239 |
| Reference:
|
[8] D. Stanovský: Homomorphic images of subdirectly irreducible groupoids.Comment. Math. Univ. Carolinae 42 (2001), 443–450. MR 1859591 |
| Reference:
|
[9] M. Yoeli: Subdirectly irreducible unary algebras.Am. Math. Mon. 74 (1967), 957–960. Zbl 0153.33802, MR 0228293, 10.2307/2315275 |
| . |
